Geodesic ham-sandwich cuts

Prosenjit Bose, Erik D. Demaine, Ferran Hurtado, John Iacono, Stefan Langerman, Pat Morin

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m+r + b. A ham-sandwich geodesic is a shortest path in P between any two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
    Pages1-9
    Number of pages9
    StatePublished - 2004
    EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
    Duration: Jun 9 2004Jun 11 2004

    Other

    OtherProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
    CountryUnited States
    CityBrooklyn, NY
    Period6/9/046/11/04

    Fingerprint

    Sandwich
    Geodesic
    Trees (mathematics)
    Bisect
    Simple Polygon
    Shortest path
    Interior

    Keywords

    • Geodesics
    • Ham-sandwich
    • Shortest paths
    • Simple polygons

    ASJC Scopus subject areas

    • Software
    • Geometry and Topology
    • Safety, Risk, Reliability and Quality
    • Chemical Health and Safety

    Cite this

    Bose, P., Demaine, E. D., Hurtado, F., Iacono, J., Langerman, S., & Morin, P. (2004). Geodesic ham-sandwich cuts. In Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) (pp. 1-9)

    Geodesic ham-sandwich cuts. / Bose, Prosenjit; Demaine, Erik D.; Hurtado, Ferran; Iacono, John; Langerman, Stefan; Morin, Pat.

    Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). 2004. p. 1-9.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Bose, P, Demaine, ED, Hurtado, F, Iacono, J, Langerman, S & Morin, P 2004, Geodesic ham-sandwich cuts. in Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). pp. 1-9, Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04), Brooklyn, NY, United States, 6/9/04.
    Bose P, Demaine ED, Hurtado F, Iacono J, Langerman S, Morin P. Geodesic ham-sandwich cuts. In Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). 2004. p. 1-9
    Bose, Prosenjit ; Demaine, Erik D. ; Hurtado, Ferran ; Iacono, John ; Langerman, Stefan ; Morin, Pat. / Geodesic ham-sandwich cuts. Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). 2004. pp. 1-9
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    AU - Morin, Pat

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